Telescoping method, summation formulas, and inversion pairs

Qing-Hu Hou; Yarong Wei; Qing-Hu Hou; Yarong Wei

doi:10.3934/era.2021007

Electronic Research Archive

2021, Volume 29, Issue 4: 2657-2671. doi: 10.3934/era.2021007

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Telescoping method, summation formulas, and inversion pairs

Qing-Hu Hou ,
Yarong Wei ^,

School of Mathematics, Tianjin University, Tianjin 300350, China

Received: 01 May 2020 Revised: 01 November 2020 Published: 11 January 2021
33F10, 05A19

Based on Gosper's algorithm, we present an approach to the telescoping of general sequences. Along this approach, we propose a summation formula and a bibasic extension of Ma's inversion formula. From the formulas, we are able to derive several hypergeometric and elliptic hypergeometric identities.
- Telescoping method,
- Gosper's algorithm,
- inversion pair,
- basic hypergeometric series,
- elliptic hypergeometric series
Citation: Qing-Hu Hou, Yarong Wei. Telescoping method, summation formulas, and inversion pairs[J]. Electronic Research Archive, 2021, 29(4): 2657-2671. doi: 10.3934/era.2021007

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Abstract

Based on Gosper's algorithm, we present an approach to the telescoping of general sequences. Along this approach, we propose a summation formula and a bibasic extension of Ma's inversion formula. From the formulas, we are able to derive several hypergeometric and elliptic hypergeometric identities.

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